Why does the "Checker Texture" node produce flicker with "Texture Coordinates Object"?
That's simply because your plane is between 2 checkers.
The checker texture is a 3D texture which alternates also in the Z axis. If you go in edit mode and move your plane up and down you will see that.
You can also rotate it to get different patterns.

In "Generated" coordinates your plane is in the vertical middle of a checker. That's why there's no artifact there.